ieee transactions on power electronics, vol. 27, no. 6...

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 6, JUNE 2012 2783

A Transformerless D-STATCOM Basedon a Multivoltage Cascade Converter

Requiring No DC SourcesKenichiro Sano, Member, IEEE, and Masahiro Takasaki, Senior Member, IEEE

Abstract—This paper deals with a cascaded multilevel converterwhich has multiple dc voltage values (multivoltage cascade con-verter or hybrid multilevel converter) for a 6.6-kV transformer-less distribution static synchronous compensator (D-STATCOM).A control method is proposed to realize dc voltage regulationof series-connected multiple cells in the STATCOM operation,making it possible to remove dc sources from all H-bridge cells.The simplified configuration without the dc sources makes theSTATCOM small and lightweight. A downscaled STATCOM modelrated at 220 V and 10 kVA is built and a series of verification tests isexecuted. Theoretical analysis and experimental results prove thestable operating performance of the proposed method in steadystates and transient states.

Index Terms—Cascaded multilevel converter, dc voltage con-trol, silicon carbide device, static synchronous compensator(STATCOM), transformerless converter.

I. INTRODUCTION

IN RECENT years, installed capacity of distributed genera-tions such as residential photovoltaic systems is increasing.

They are often connected to the distribution grid. Since their out-put power is affected by solar irradiance, the power flow mayfluctuate and be bidirectional in the grids. As a result, voltagemanagement of the grids may become difficult in the area wherephotovoltaic systems are densely installed [1].

The static synchronous compensator (STATCOM) is a vitalsolution to maintain grid voltages by supplying or consum-ing reactive power. It has been installed in the transmissiongrids, and its use is spreading to the medium-voltage distributiongrids as a distribution STATCOM (D-STATCOM). The existingD-STATCOM is equipped with a step-down transformer and anac filter. In this case, the transformer and the filter inductorsmake the STATCOM bulky and heavy. For example, the weightof a prototype D-STATCOM rated at 360 kVA was 3000 kg [2].It is estimated that its transformer weighs 1000 kg, and its acinductors weigh 400 kg. Therefore, further reduction of volumeand weight is required for the practical installation in the urbanarea.

Manuscript received July 20, 2011; revised September 6, 2011; acceptedOctober 25, 2011. Date of current version March 16, 2012. This paper waspresented at the IEEE Energy Conversion Congress and Exposition, Phoenix,AZ, September 17–22, 2011. Recommended for publication by Associate EditorR. Burgos.

The authors are with the System Engineering Research Laboratory, CentralResearch Institute of Electric Power Industry, Komae-shi, Tokyo 201-8511,Japan (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2011.2174383

Cascaded multilevel converters have been studied to realizea small and lightweight STATCOM [3], [4]. A single-phasefull-bridge or “H-bridge” inverter is a fundamental buildingblock and it is called as a “cell.” The identical cells are con-nected in series and the string composes a cascaded multilevelconverter (called as “single-voltage cascade converter” in thispaper). Since the cascade converter realizes high blocking volt-age and low-harmonic output voltage, it needs no step-downtransformers for medium-voltage applications.

A cascaded multilevel converter which has more than twotypes of cells with different rated voltages (multivoltage cascadeconverter or hybrid multilevel converter) has been proposedin [5]–[7]. Different cells whose dc voltage ratio is typically2:1 or 3:1 are connected in series and controlled together tocompose low-harmonic output voltage. It can reduce voltageharmonics comparing to the single-voltage cascade converterwith the same number of cells.

On the other hand, the multivoltage cascade converter hasdifficulty in maintaining the dc voltage ratio to the predeter-mined value. Although it is confirmed that the dc sources con-sisting of isolated power supplies are effective to keep the dcvoltages [5]–[7], the method needs power supplies in all cellsand makes its configuration complex. The power supplies re-quiring high voltage isolation also makes the converter bulky.However, the dc sources are not essential for a STATCOM ap-plication. Control methods have been proposed to remove somedc sources by utilizing redundant switching patterns [8] and allpower supplies by disabling the pulse width modulation (PWM)control [9], which may increase some amount of output voltageharmonics.

This paper proposes a new dc voltage control method forthe multivoltage cascade converter. The control method realizesenergy transfer between the series connected different cells dur-ing STATCOM operation. Combining with feedback controller,it can maintain all dc voltages to the predetermined referencevalue without dc sources. A downscaled STATCOM model ratedat 220 V and 10 kVA is built and a series of verification testsis executed. Theoretical analysis and experimental results provethe stable operating performance of the proposed method in thestartup, steady states, and transients under voltage sags.

II. MULTIVOLTAGE CASCADE CONVERTERS

A. System Configuration

Fig. 1 represents a circuit configuration of multivoltage cas-cade converters. The converter consists of three clusters with

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Fig. 1. STATCOM based on a multivoltage cascade converter.

star configuration, and each of the clusters consists of threeseries-connected H-bridge cells which have different dc volt-ages from each other. These cells are described as “high voltage(HV) cell,” “medium voltage (MV) cell,” and “low voltage (LV)cell” in descending order of their dc voltages. The cells hav-ing higher dc voltage share larger conversion power with lowerswitching frequency. There are some options in the dc voltageratio among vC H y , vC M y , and vC Ly (subscript y is either u, v,or w) . One typical ratio is vC H y : vC M y : vC Ly = 4 : 2 : 1 [5],[8]–[10], and other ratios such as 9 : 3 : 1 and 6 : 2 : 1 are alsoinvestigated in [11]–[13]. vC H y : vC M y : vC Ly = 6 : 2 : 1 isan optimum dc voltage ratio to obtain maximum output volt-age levels under PWM operation of LV cells [12]. Based onthe optimum ratio, the dc voltage ratio in this paper is set tovC H y : vC M y : vC Ly = 6 : 2 : 1.2, where vC Ly is increased by20% in order to apply a control method proposed in this pa-per. The references of dc voltages are v∗

C H y = 6Vdc , v∗C M y =

2Vdc , and v∗C Ly = 1.2Vdc using unit dc voltage Vdc . Vdc is set to

0.6 kV for 6.6-kV utility and industrial distribution systems, andeach dc voltage is vC H y = 3.6 kV, vC M y = 1.2 kV, and vC Ly =0.72 kV. Then, HV, MV, and LV cells can be composed of powerdevices rated at 6.5, 2.5, and 1.2 kV in blocking voltage, respec-tively. The LV cells operating with PWM can increase theirswitching frequency or reduce their switching loss by applyingup-to-date 1.2-kV SiC-JFET [14] or SiC-MOSFETs [15], [16].

B. Output Voltage Synthesis

As well as single-voltage cascade converters, the multivoltagecascade converter operates each of the clusters as a single-phaseconverter, and three clusters together as a three-phase converter.Therefore, its control method above the cluster level is the sameas the single-voltage cascade converters.

Fig. 2. Output voltage waveforms of each cell in the multivoltage cascadeconverter whose dc voltage ratio is 6 : 2 : 1.2.

On the other hand, output voltage synthesis in a cluster ischaracteristic to the multivoltage cascade converter because theoutput pulses of the HV, MV, and LV cells have different ampli-tudes. The control method discussed here and in the next sectionis independently applied to each of the clusters. Therefore, allvariables mean the value for the same phase and their subscripty is removed for simplicity.

Fig. 2 shows the output voltage waveforms of each cell with anearest level modulation [13]. The output voltage reference v∗

outis a sinusoidal waveform whose amplitude is less than 9Vdc . Theoutput voltage of the HV cell vH and that of the MV cell vM areselected to make their total value vH + vM be a nearest to v∗

out .Then the HV cell outputs one positive and one negative pulses,and the MV cell outputs five positive and five negative pulsesduring a cycle. The mean output voltage of LV cell vL outputsthe remainder of v∗

out , and it is given as follows:

vL = v∗out − vH − vM . (1)

The LV cell outputs vL in average with high frequency PWM.Then, vL exists in the following range:

−Vdc ≤ vL ≤ Vdc . (2)

C. DC Voltage Imbalance and Conventional Solutions

An ideal STATCOM does not supply/consume active powerbecause the output voltage vout and the output current i are inquadrature. Also in the each cell level, the mean values of dcvoltages vC H , vC M , and vC L do not change under the idealcondition. However, in reality, the dc voltages vary when someamount of active power flows into the converter to compensateits power loss. The active power is nonlinearly distributed toeach cell according to the voltage modulation index, whichcauses the dc voltage imbalance in the multivoltage cascadeconverter [13]. Transient nonperiodic current and variation ofdevice characteristics may also cause the dc voltage imbalance.

DC sources consisting of isolated power supplies can main-tain the dc voltages when they are connected to all dc capacitors

SANO AND TAKASAKI: TRANSFORMERLESS D-STATCOM BASED ON A MULTIVOLTAGE CASCADE CONVERTER 2785

TABLE IOUTPUT VOLTAGE OF EACH CELL IN THE MULTIVOLTAGE CASCADE CONVERTER WHOSE DC VOLTAGE RATIO IS 6 : 2 : 1.2

[5]–[7]. However, the dc sources need high-voltage isolationamong themselves and bidirectional power flow, making theconverter bulky. The number of the dc sources can be reducedby applying novel modulation strategies to series connected twocells [17]–[19] and three cells [20] for motor drive and renewableenergy applications. For STATCOM applications, the number ofthe dc sources can be reduced to three by utilizing redundantswitching patterns [8]. All dc sources can be removed by in-creasing redundant switching patterns in case the PWM is notused [9], which may increases low-order harmonics comparingto the PWM method.

III. PROPOSED OUTPUT VOLTAGE SYNTHESIS AND ENERGY

TRANSFER CONTROL IN A CLUSTER

The proposed control method in this paper realizes energytransfer among HV, MV, and LV cells under PWM control withsynthesizing low-harmonic output voltage. The control enablesthe voltage balancing of the dc capacitors CH , CM , and CL

together with voltage feedback controllers described in the Sec-tion IV, resulting in requiring no dc sources.

Table I shows the output voltages of each cell in a multivolt-age cascade converter. According to the output voltage referencev∗

out , the voltages vH , vM , and vL are selected from nine com-binations. Parameters ΔV ′

H M , ΔV ′H L , and ΔV ′

M L influence theboundary levels to switch the output voltages, making it possi-ble to transfer the energy among CH , CM , and CL in the samecluster. When ΔV ′

H M , ΔV ′H L , and ΔV ′

M L are set to zero, thecontrol is the same as the conventional nearest voltage modula-tion transferring no energy among CH , CM , and CL .

A. Energy Transfer Between Two Cells

1) Energy Transfer Between the HV Cell and the LV Cell: Itis assumed that a cluster operates as a single-phase STATCOMand its output voltage reference v∗

out and output current i are thefollowing sinusoidal waveforms:

v∗out = 9Vdc sin ωt (3)

i = I cos ωt (4)

where 9Vdc and I are the amplitude of v∗out and i, respectively.

Fig. 3. Input power of each cell during energy transfer from the HV cell tothe LV cell. Solid line is in case ΔVH L > 0, and the dotted line is in caseΔVH L =0. ΔVH M = ΔVM L = 0 in both cases.

A parameter ΔVH L is introduced for the energy transfer be-tween the HV cell and the LV cell. Polarity of ΔV ′

H L is selectedaccording to the output current i as follows:

ΔV ′H L = ΔVH L · sgn(i) (5)

where the sign function sgn(x) is defined as

sgn(x) =

⎧⎪⎨

⎪⎩

−1 if x < 0

0 if x = 0

1 if x > 0.

(6)

Other parameters are set as ΔVH M = ΔVM L = 0. These valuesgive a set of vH , vM , and vL according to Table I.

Fig. 3 shows the voltage and instantaneous power waveformsin case ΔVH L = 0 (shown by dotted lines) and ΔVH L > 0(shown by solid lines). The products of the output current i andthe output voltages vH , vM , and vL are instantaneous power


Fig. 4. Input power of each cell during energy transfer from the HV cell tothe MV cell. Solid line is in case ΔVH M > 0, and the dotted line is in caseΔVH M =0. ΔVH L = ΔVM L = 0 in both cases.

flowing into the HV, MV, and LV cells, shown by pH , pM , andpL , respectively. ΔpH , ΔpM , and ΔpL are differences betweensolid and dotted lines in pH , pM , and pL . Averages of ΔpH ,ΔpM , and ΔpL in a cycle are the received power of the HV,MV, and LV cells, shown by PH , PM , and PL , respectively.

The theoretical analysis of PH , PM , and PL gives (see theAppendix)

PH = − 43π

ΔVH LI (7)

PM = 0 (8)

PL =43π

ΔVH LI. (9)

This result means that energy transfer from the HV cell to theLV cell is controlled by ΔVH L .

The range of vL expands according to ΔVH L as follows:

−Vdc − |ΔVH L | ≤ vL ≤ Vdc + |ΔVH L |. (10)

To make the LV cell able to output the voltage in the range of(10), the dc voltage of the LV cell vC L should be maintained as

vC L ≥ Vdc + |ΔVH L |. (11)

2) Energy Transfer Between the HV Cell and the MV Cell:A parameter ΔVH M is used for the energy transfer between theHV cell and the MV cell. A set of vH , vM , and vL is obtainedby Table I and ΔV ′

H M which is given by

ΔV ′H M = ΔVH M · sgn(i). (12)

Fig. 4 shows the voltage and instantaneous power waveformsin case ΔVH M = 0 (shown by dotted lines) and ΔVH M > 0(shown by solid lines). Other parameters are set as ΔVH L =ΔVM L = 0.

Fig. 5. Input power of each cell during energy transfer from the MV cell tothe LV cell. Solid line is in case ΔVM L > 0, and the dotted line is in caseΔVM L =0. ΔVH M = ΔVH L = 0 in both cases.

The theoretical analysis of PH , PM , and PL gives

PH = − 43π

ΔVH M I (13)

PM =43π

ΔVH M I (14)

PL = 0. (15)

This result means that energy transfer from the HV cell to theMV cell is controlled by ΔVH M .

The range of vL expands according to ΔVH M as follows:

−Vdc − |ΔVH M | ≤ vL ≤ Vdc + |ΔVH M |. (16)


vC L ≥ Vdc + |ΔVH M |. (17)

3) Energy Transfer Between the MV Cell and the LV Cell:A parameter ΔVM L is used for the energy transfer between theMV cell and the LV cell. A set of vH , vM , and vL are obtainedby Table I and ΔV ′

H M which is given by

ΔV ′M L = ΔVM L · sgn(i). (18)

Fig. 5 shows the voltage and instantaneous power waveformsin case ΔVM L = 0 (shown by dotted lines) and ΔVM L > 0(shown by solid lines). Other parameters are set as ΔVH M =ΔVH L = 0.

The theoretical analysis of PH , PM , and PL gives

PH = 0 (19)

PM = − 43π

ΔVM LI (20)

PL =43π

ΔVM LI. (21)


This result means that energy transfer from the MV cell to theLV cell is controlled by ΔVM L .

The range of vL expands according to ΔVM L as follows:

−Vdc − |ΔVM L | ≤ vL ≤ Vdc + |ΔVM L |. (22)


vC L ≥ Vdc + |ΔVM L |. (23)

B. Energy Transfer Among Three Cells

Energy transfer among three cells is also realized by givingtwo parameters among ΔVH L , ΔVH M , and ΔVM L together.For example, control of ΔVH L and ΔVH M realizes energytransfer among three cells because the MV cell and the LV cellcan transfer their energy by way of the HV cell. Then, the rangeof vL is expressed by (10), (16), and the following equation:

−Vdc − |ΔVH L + ΔVH M | ≤ vL ≤ Vdc + |ΔVH L + ΔVH M |.(24)

To make the LV cell able to output the voltage in the range of(24), the dc voltage of the LV cell vC L should be maintained tosatisfy (11), (17), and the following equation:

vC L ≥ Vdc + |ΔVH L + ΔVH M |. (25)

C. DC Voltage Ratio for the Proposed Control

In Section II-A, vC L was increased by 20% from Vdc to ap-ply the proposed energy transfer control. However, the increaseis not necessarily 20% but arbitrary value as long as satisfy-ing (11), (17), (23), and (25). ΔVH L , ΔVH M , and ΔVM L aremuch smaller than Vdc under usual operating conditions as aSTATCOM, because the required amount of energy transfer in acluster is small. Hence, 1.2Vdc is large enough for vC L to satisfythe conditions.

Although the dc voltage ratio aforementioned was 6 : 2 : 1.2,the proposed method is applicable for other voltage ratios suchas 5 : 2 : 1.2 and 4 : 2 : 1.2. Furthermore, the proposed methodis applicable if the ratio satisfies the modulation condition in-vestigated in [12]: any pair of adjacent voltage levels can bemodulated by switching only the LV cell. However, Table I hasto be modified according to each of the dc voltage ratio.

When the output voltage is not enough for connecting grids,the voltage can be expanded with additional HV cells. Four-cellconfiguration whose dc voltage ratio is 6 : 6 : 2 : 1.2 includingtwo HV cells can output up to ac 11 kV. Similarly, a configu-ration including three HV cells can achieve ac 15 kV, and fourHV cells can achieve 20 kV. In these configurations, the HVcells’ switching angles are shifted each other like single-voltagecascade converters to synthesize low harmonic voltage wave-form [3], [21], [22].

IV. CONTROL METHOD FOR A STATCOM BASED

ON A MULTIVOLTAGE CASCADE CONVERTER

Fig. 6 shows an overall control block diagram for the pro-posed STATCOM based on a multivoltage cascade converter.The fundamental architecture is based on three function blocks

developed for single-voltage cascade converters [4], [23], that isa decoupled current control, a clustered balancing control, andan individual balancing control. Main differences for a multi-voltage cascade converter are as follows.

1) Energy stored in the dc capacitors is calculated and usedfor control values instead of the dc capacitor voltages.

2) Individual balancing control is modified to accommodatemultivoltage cascade converters.

Each block is explained in detail next.

A. Control Scheme Based on the Energy Storedin the DC Capacitors

Balancing controls are constructed based on the energy storedin the dc capacitor. As a result, deviations from the reference val-ues can be quantitatively compared among cells having differentcapacitances and voltages, which is effective for multivoltagecascade converters.

Energy stored in the dc capacitor EC xy is given by

EC xy =12CxV 2

C xy (26)

where Cx is the capacitance and VC xy is the sensed dc capacitorvoltage (subscript x is either H , M , or L). A reference of thestored energy E∗

C x is calculated from its voltage reference V ∗C x

by

E∗C x =

12CxV ∗

C x2 . (27)

The individual balancing control regulates the stored energyEC xy to be equal to its reference value E∗

C x .Total energy stored in the cluster is given by

EC y = EC H y + EC M y + EC Ly (28)

where EC H y , EC M y , and EC Ly are the energies stored in theHV, MV, and LV cells, respectively. The clustered balancingcontrol regulates EC u , EC v , and EC w to balance each other.

Total energy stored in the converter EC is given by

EC = EC u + EC v + EC w . (29)

Reference of the energy stored in the converter E∗C is calculated

using the values given by (27) as follows:

E∗C = 3(E∗

C H + E∗C M + E∗

C L ). (30)

The decoupled current control regulates EC to be equal to itsreference value E∗

C .

B. Decoupled Current Control

Fig. 7 shows a block diagram of the decoupled current con-trol [23], [24]. The decoupled current control regulates instan-taneous active and reactive power by considering a set of threeclusters as a three-phase converter. The total stored energy in theconverter is also regulated in this block. Output currents iu , iv ,iw and ac line voltages vSu , vSv , and vSw are transformed to thed–q rotating coordinate as id , iq , vSd , and vSq . A proportionalcontroller whose gain is KC calculates the reference of instan-taneous active power p∗ based on the deviation between EC andits reference E∗

C . A reference of instantaneous reactive power


Fig. 6. Control block diagram for the STATCOM based on a multivoltage cascade converter.

Fig. 7. Decoupled current control for a three-phase converter.

q∗ is given by a system operator from the outside of this controlblock. Dividing p∗ and q∗ by the ac line voltage vSd gives theoutput current references i∗d and i∗q , which are calculated by

i∗d =KC (E∗

C − EC )vSd

(31)

i∗q =q∗

vSd. (32)

Proportional and integral controller decides the output voltagesfrom the deviation between the references i∗d , i∗q and the actualcurrents id , iq . The ac line voltage and voltage across the acinductor LAC are added to the output voltage reference in thefeed-forward manner. Therefore, voltage references v∗

d and v∗q

are given by

[v∗

d

v∗q

]

=[

vSd

vSq

]

+[

0 ωLAC−ωLAC 0

] [id

iq

]

− KI

[i∗d − id

i∗q − iq

]

− KI

TI

∫ [i∗d − id

i∗q − iq

]

dt (33)

where KI and TI are a proportional gain and a time constant ofthe current controller, respectively. The values are transformedto the three-phase voltage references v∗

u , v∗v , and v∗

w by an inversed–q transformation.

C. Clustered Balancing Control

Fig. 8 shows a block diagram of the clustered balancing con-trol proposed in [25] and [26]. This control block operates tobalance the energy stored in each cluster by considering a set ofHV, MV, and LV cells as a single-phase converter. It injects afundamental-frequency zero-sequence voltage v0 to the voltagereferences v∗

u , v∗v , and v∗

w [25]. Although the injection of a zero-sequence voltage v0 causes no change in the line-to-line voltageand line currents, it allows us to transfer active power amongclusters. Here, ΔEC u , ΔEC v , and ΔEC w are the degree of im-balance of the energy stored in the cluster, and their three-phaseto two-phase transformation gives ΔEC α and ΔEC β . They are


Fig. 8. Clustered balancing control between three clusters in a converter.

Fig. 9. Individual balancing control between three cells in a cluster.

calculated by

[ΔEC α

ΔEC β

]

=

√23

⎡

⎢⎢⎣

1 −12

−12

0√

32

−√

32

⎤

⎥⎥⎦

⎡

⎢⎢⎢⎢⎢⎢⎣

13EC − EC u

13EC − EC v

13EC − EC w

⎤

⎥⎥⎥⎥⎥⎥⎦

.

(34)Reference of the zero-sequence voltage v∗

0 is given by

v∗0 = K0

√ΔE2

C α + E2C β ·

√2 sin(ωt + φ0) (35)

φ0 = tan−1 iqid

− tan−1 EC β

EC α(36)

where K0 is a proportional gain for the amplitude regulation ofv∗

0 , and φ0 is the phase angle of v∗0 .

D. Individual Balancing Control

Fig. 9 shows a block diagram of the proposed individualbalancing control. This control maintains the dc voltage ratioof the HV, MV, and LV cells by applying the energy transfermethod proposed in Section III. Fig. 9 depicts a block for asingle cluster, and two more identical controllers are structuredfor other two clusters.

Reference of the energy stored in the MV cell E∗C M y is de-

rived from the total energy of the cluster EC y and the ratio ofreferences E∗

C /3 and E∗C M as follows:

E∗C M y =

3E∗C M

E∗C

EC y . (37)

A feedback controller provides ΔVH M y from the error between

TABLE IICIRCUIT AND CONTROL PARAMETERS OF THE EXPERIMENTAL SETUP

the reference E∗C M y and actual EC M y as follows:

ΔVH M y = KC M (E∗C M y − EC M y ) (38)

where KC M is a proportional gain. In the same manner, E∗C Ly

is given by

E∗C Ly =

3E∗C L

E∗C

EC y . (39)

ΔVH Ly is calculated by a proportional gain KC L , the referencevalue E∗

C Ly , and the actual value EC Ly as follows:

ΔVH Ly = KC M (E∗C Ly − EC Ly ). (40)

ΔVH M y and ΔVH Ly are immediately reflected to Table I. Then,the cluster operates to maintain its dc voltage ratio.

Although a pair of ΔVH M y and ΔVH Ly are used in theaforementioned explanation, a pair of ΔVH Ly and ΔVM Ly , orΔVM Ly and ΔVH M y are also available instead of ΔVH M y andΔVH Ly in order to maintain the dc voltage ratio.

V. EXPERIMENTAL RESULTS

A. Experimental Setup

A three-phase downscaled STATCOM rated at 220 V and10 kVA was built and tested in the circuit configuration shownin Fig. 1. Table II and Fig. 10 show circuit parameters and a pho-tograph of the experimental setup, respectively. Si-MOSFETs(rated at 250 V for HV cells, 100 V for MV cells, and 60 V forLV cells) were applied to the circuit instead of insulated gatebipolar transistors (IGBTs). The dc capacitors were designed to


Fig. 10. Experimental setup.

make their voltage ripple less than 10% in the rated power, andalso to meet their current ripple rating. Starting resistors weretemporarily inserted in series with ac inductors for pre-chargingthe dc capacitors before switching operation.

The controller consists of a digital signal processor (DSP)(Texas Instruments TMS320C6713, 32-bit, floating point, 225MHz clock), an field programmable gate array (FPGA) (XilinxSpartan-3, 1.5 M system gates), and two AD converters (AnalogDevices AD7266, 12-bit, 12-channel analog inputs). Its sam-pling and calculation interval was 50 μs. Current control gainKI and time constant TI were determined based on the experi-mental tests to achieve stable transient response. Control gainsfor the energy stored in capacitor KC , K0 , KC M , and KC L

were designed based on their startup operation characteristicsto have slower response than the inner-loop current controller.

B. Startup Operation

Fig. 11 shows experimental waveforms when the STATCOMwas starting up. The bold, solid, and dotted lines show the valuesof u-phase, v-phase, and w-phase, respectively.

Fig. 11(a) shows the waveforms when the converter was con-nected to an ac source. Although all MOSFETs were off-state,the ac current was rectified by the antiparallel diodes. The cur-rent charged dc capacitors by way of 5.6 Ω starting resistor. Thedc capacitors were charged about 80% of the reference voltageduring this mode. Since dc capacitors of the same cluster areconnected in series in this mode, the dc voltage ratio can bemaintained by simply setting their capacitances as

CH : CM : CL =1

V ∗C H

:1

V ∗C M

:1

V ∗C L

. (41)

The capacitances CM and CL can be reduced according to theirvoltage and current ripple if a control to maintain the dc voltageratio during the precharge is employed.

Fig. 11(b) shows the waveforms after starting the switchingoperation. The reactive power q was increased to 10 kVA in100 ms. Although some amount of voltage imbalance was ob-served during transient state, all dc voltages converged to thereference value in 200 ms.

Fig. 11. Experimental waveforms during startup. (a) Pre-charging throughstarting resistor. (b) Startup of the converter switching.

C. Steady-State Operations

Fig. 12 shows the output voltage and current waveforms whenthe STATCOM was put into capacitive operation at 10 kVA.Phase angle of the output voltage vout-u lags to that of the outputcurrent iu by π/2 rad. The HV, MV, and LV cells operated at50 Hz, 250 Hz, and 10 kHz switching, and composed vout-uhaving 19 voltage levels. Total harmonic distortion (THD) ofiu was 1.4%, which is small enough to grid-tie requirement.Although vout-u had some 1 μs glitches caused by the deadtime, the glitches scarcely affected the output current.

Fig. 13 shows the output voltage and current waveforms whenthe STATCOM was put into inductive operation at 10 kVA.vout-u had 17 voltage levels because the output voltage of theconverter was slightly reduced resulting from the voltage dropsin the ac inductors LAC . Phase angle of iu lags to that of vout−u

by π/2 rad, and the THD of iu was 1.1%.


Fig. 12. Experimental waveforms with capacitive operation at 10 kVA.

Fig. 13. Experimental waveforms with inductive operation at 10 kVA.

Fig. 14 shows the output voltage/current and dc capacitorvoltage waveforms when the output power q was changed fromcapacitive to inductive operation at 10 kVA in 20 ms. The meanvalues of the dc voltages vC H y , vC M y , and vC Ly are maintainedto their reference values by the proposed dc voltage controls.

D. DC Voltage Control Characteristics

Fig. 15 shows the waveforms when the dc voltage controlswere intentionally disabled during operation in order to confirmthe necessity of the control. After disabling the dc voltage con-trols, vC M y started to increase and vC H y and vC Ly started todecrease, resulting in the voltage imbalance in a cluster. The im-balance caused distortion in the output current iy . Since vC M v

reached to 120% of the reference voltage 180 ms after the dis-abling, overvoltage protection halted the converter. This resultshows the necessity of the dc voltage controls for the converteroperation.

Fig. 14. Experimental waveforms during changing from capacitive to induc-tive operation at 10 kVA.

Fig. 15. Experimental waveforms after intentionally disabling the dc voltagecontrols.

E. Operation Characteristics Under Voltage Sags

Fig. 16 shows the experimental setup to confirm the STAT-COM’s operation characteristics under voltage sags. Typicalvoltage sags were emulated by a voltage sag generator con-sisting of an autotransformer and bidirectional semiconductorswitches [27], [28]. A transformer is inserted between the volt-age sag generator and the STATCOM in order to simulate boththe voltage sags and the phase jumps in an ungrounded distri-bution line caused by a fault in high-voltage transmission lines.

Fig. 17 shows the experimental results during three-phase80% voltage sag. The sag continued for 500 ms. The STATCOM


Fig. 16. Experimental setup for simulating voltage sag.

Fig. 17. Experimental results during a three-phase 80% voltage sag condition.

reduced its output current to zero under such a severe voltage sagin order to avoid voltage overshoot just after the fault clearing.LV and MV cells continued their switching to control the outputcurrent to zero. HV cells did not switch during the sag becausethe line voltage was low. When the line voltage recovered after500 ms, the STATCOM rapidly regained its output current. Thedc voltages were kept almost constant during the operation.

Fig. 18 shows the possible voltage sag patterns in the distri-bution lines caused by a single-phase fault in the transmissionline. The voltage sag changes according to the transformer’swinding connection [29]. When the Y–Y transformer is used inthe substation, zero-phase-sequence voltage is eliminated in thedistribution line. Then, the phase angle of vSv and vSw jumps to-gether. When the Y–Δ transformer is used in the substation, vSu

and vSv drop and their phase angle also jumps in the distributionline. Both cases were verified by the experiments.

Fig. 19 shows the experimental results during a single-phase80% voltage sag assuming that the Y–Y transformer is used inthe distribution substation. Fig. 20 shows the case that the Y–Δtransformer is used. Both of them continued their switching andkept the line currents to zero. The dc voltages did not deviatedfrom the reference values and the STATCOM was able to regainits output current after the recovery of line voltage.

Fig. 18. Voltage sags in the distribution grid caused by the single-phase faultin the transmission grid.

Fig. 19. Experimental results during a single-phase 80% voltage sag by wayof a Y–Y transformer.

While the output current was reduced to zero during the sag inthe experiment, the STATCOM has capability to keep its outputcurrent flowing in the three-phase balanced voltage sag shownin Fig. 17. Because the output voltage and output current of allclusters can be in quadrature, they cause no active power flow.However, the STATCOM cannot keep its output current flowingin the three-phase unbalanced voltage sags shown in Figs. 19and 20. This is because some amount of active power flowsinto the clusters, and the stored energy in the clusters becomesimbalanced.

VI. CONCLUSION

This paper has proposed a system configuration and a con-trol method for a multivoltage cascade converter in order


Fig. 20. Experimental results during a single-phase 80% voltage sag by wayof a Y–Δ transformer.

to reduce power loss and volume of a 6.6-kV transformer-less D-STATCOM. The proposed system has the followingcharacteristics.

1) The cascaded H-bridge configuration realizes direct con-nection to the 6.6-kV distribution lines without step-downtransformers.

2) The multivoltage cascade configuration reduces outputvoltage harmonics, resulting in a reduction of ac filters.

3) Only the cells having lowest dc voltage (0.72 kV) operatein high frequency PWM, resulting in a reduction of overallswitching loss and low-order harmonics.

4) The cells having highest dc voltage (3.6 kV) consist ofhigh blocking voltage IGBTs, resulting in a reduction ofcascaded numbers and conduction loss.

5) The reduction of switching and conduction loss downsizesthe heat dissipation system.

The proposed dc voltage balancing control method for themultivoltage cascade converter realizes to remove the auxiliarydc sources from all cells during STATCOM operation. Thiscontrol realizes the energy transfer among the cells in the samephase by increasing dc voltage of the LV cell by 20%, and adjust-ing the phase angle of the output voltage pulses. A downscaledexperimental model rated at 220 V and 10 kVA was built andtested. The experimental results proved the stable operation inthe startup, steady state, and output power change of the pro-posed method. Fundamental fault ride through capability wasalso verified by the experiments.

Fig. 21. Relationship between the output voltage reference and the time toswitch the output voltage patterns.

APPENDIX

ANALYSIS OF THE TRANSFERRED POWER

This section deals with the analysis on the averaged trans-ferred power among cells. The output voltage v∗

out and currenti are in quadrature during STATCOM operation as follows:

vout = 9Vdc sin ωt (42)

i = I cos ωt. (43)

Since the waveforms are symmetrical, the following analysis iscarried out in a range of 0 ≤ t ≤ π/2ω (a quarter cycle). ΔVx

is the variation of the output voltage Vx during a short periodΔtx from t = tx to t = tx + Δtx , and the relation is describedas follows:

ΔVx

Δtx= 9Vdcω cos ωtx. (44)

Fig. 21 shows the relation among the output voltage referencev∗

out , the threshold to switch the output voltages of the cells Vdc ,3Vdc , 5Vdc , 7Vdc , and the time to switch the output voltage ta , tb ,tc , td . It is assumed that the parameters ΔVH M = ΔVM L = 0.When ΔVH L is used for the control parameter, the HV cellswitches at v∗

out = 3Vdc + ΔV ′H L according to Table I. Then,

the switching delays for Δtb . According to (44), the relation isgiven by

ΔVH L

Δtb= 9Vdcω cos ωtb. (45)

PH is the average power flowing into the HV cell, which is theproduct of the HV cell’s output voltage 6Vdc , the output currenti, and the period Δtb divided by a quarter cycle π/2ω. It is givenby

PH = −6Vdc · I cos ωtb · Δtbπ/2ω

. (46)

Substituting (45) for (46) yields

PH = − 43π

ΔVH LI. (47)


The MV cell switches at v∗out = Vdc + ΔVH L , v∗

out =3Vdc + ΔVH L , and v∗

out = 5Vdc + ΔVH L . Then, the switch-ing delays for Δta , Δtb , and Δtc , respectively. The averagepower flowing into the MV cell PM is given by

PM = −2Vdc · I cos ωta · Δtaπ/2ω

+4Vdc · I cos ωtb · Δtb

π/2ω

− 2Vdc · I cos ωtc · Δtcπ/2ω

= (−2Vdc + 4Vdc − 2Vdc)2ΔVH LI

9πVdc

= 0. (48)

Total power of the HV, MV, and LV cells is zero in a cyclebecause the converter’s output voltage vout and current i are inquadrature. That is expressed as

PH + PM + PL = 0. (49)

Equations (47)–(49) yield the average power flowing into theLV cell PL as follows:

PL = −PH − PM

=43π

ΔVH LI. (50)

The analysis shows that the operation of ΔVH L causes energytransfer from the HV cell to the LV cell without any influenceon the MV cell.

It is assumed that ΔVH L = ΔVM L = 0. When ΔVH M isused to transfer power from the HV cell to the MV cell, the HVcell’s switching delays for Δtb . Then, PH is given in the samemanner by

PH = −6Vdc · I cos ωtb · Δtbπ/2ω

= − 43π

ΔVH M I. (51)

At the same time, the MV cell’s switching delays for Δtb andΔtd . Then, PM is given by

PM =4Vdc · I cos ωtb · Δtb

π/2ω+

2Vdc · I cos ωtd · Δtdπ/2ω

= (4Vdc + 2Vdc)2ΔVH M I

9πVdc

=43π

ΔVH M I. (52)

Equations (49), (51), and (52) yield the average power flowinginto the LV cell PL as follows:

PL = −PH − PM

= 0. (53)

The analysis shows that the operation of ΔVH M causes energytransfer from the HV cell to the MV cell without any influenceon the LV cell.

It is assumed that ΔVH M = ΔVH L = 0. When ΔVM L isused to transfer power from the MV cell to the LV cell, the HV

cell’s switching time does not change. That is expressed as

PH = 0. (54)

The MV cell’s switching delays for Δta , Δtc , and Δtd , respec-tively. Then, PM is given by

PM = −2Vdc · I cos ωta · Δtaπ/2ω

− 2Vdc · I cos ωtc · Δtcπ/2ω

− 2Vdc · I cos ωtd · Δtdπ/2ω

= (−2Vdc − 2Vdc − 2Vdc)2ΔVM LI

9πVdc

= − 43π

ΔVM LI. (55)

Equations (49), (54), and (55) yield the average power flowinginto the LV cell PL as follows:

PL = −PH − PM

=43π

ΔVM LI. (56)

The analysis shows that the operation of ΔVM L causes energytransfer from the MV cell to the LV cell without any influenceon the HV cell.

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Kenichiro Sano (S’07–M’10) received the B.S. de-gree in international development engineering, andthe M.S. and Ph.D. degrees in electrical and electronicengineering from the Tokyo Institute of Technology,Tokyo, Japan, in 2005, 2007, and 2010, respectively.

From 2008 to 2010, he was a Research Fellow ofthe Japan Society for the Promotion of Science. In2008, he was a Visiting Scholar at Virginia Polytech-nic Institute and State University, Blacksburg, VA,for five months. He is currently a Research Scien-tist in the System Engineering Research Laboratory,

Central Research Institute of Electric Power Industry, Komae-shi, Tokyo. Hiscurrent research interests include switched-capacitor converters and multilevelconverters.

Masahiro Takasaki (M’87–SM’10) was born onJuly 18, 1957. He received the B.E., M.E., and Dr.Eng. degrees in electrical engineering from the Uni-versity of Tokyo, Tokyo, Japan, in 1979, 1981, and1992, respectively.

After he joined Central Research Institute of Elec-tric Power Industry, Komae-shi, Tokyo, in 1981, hehas been involved with the analysis and control ofpower systems including HVdc and power electron-ics devices. He is currently a Senior Research Sci-entist at CRIEPI. Since 2005, he has been a Visiting

Professor in Advanced Energy Department, University of Tokyo.

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